The proof runs along the lines of the proof of [1]}.
For \(j\in \mathbb {N}\)  let \(_j\subset \)  be the set of all \(t\in \)  such that \(\mathcal {H}^1(K\cap E_t)>\frac{1}{j}.\)  Then by (REF ) \(_j\)  cannot contain more than \(j\mathcal {H}^1(K)\)  elements. Since \(=\cup _j _j,\)  the set \(\)  is at most countable.
